A compactness theorem for the yamabe problem

M. F. Khuri; F. C. Marques; R. M. Schoen

doi:10.4310/jdg/1228400630

A compactness theorem for the yamabe problem

M. F. Khuri, F. C. Marques, R. M. Schoen

Research output: Contribution to journal › Article › peer-review

136 Scopus citations

Abstract

In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n ≥ 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n ≥ 25.

Original language	English (US)
Pages (from-to)	143-196
Number of pages	54
Journal	Journal of Differential Geometry
Volume	81
Issue number	1
DOIs	https://doi.org/10.4310/jdg/1228400630
State	Published - 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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abstract = "In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n ≥ 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n ≥ 25.",

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AU - Marques, F. C.

AU - Schoen, R. M.

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N2 - In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n ≥ 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n ≥ 25.

AB - In this paper, we prove compactness for the full set of solutions to the Yamabe Problem if n ≥ 24. After proving sharp pointwise estimates at a blowup point, we prove the Weyl Vanishing Theorem in those dimensions, and reduce the compactness question to showing positivity of a quadratic form. We also show that this quadratic form has negative eigenvalues if n ≥ 25.

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DO - 10.4310/jdg/1228400630

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SP - 143

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JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

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A compactness theorem for the yamabe problem

Abstract

All Science Journal Classification (ASJC) codes

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